Level of Measurement - Debate On Classification Scheme

Debate On Classification Scheme

There has been, and continues to be, debates about the merits of the classifications, particularly in the cases of the nominal and ordinal classifications (Michell, 1986). Thus, while Stevens' classification is widely adopted, it is by no means universally accepted.

Duncan (1986) observed that Stevens' classification nominal measurement is contrary to his own definition of measurement. Stevens (1975) said on his own definition of measurement that "the assignment can be any consistent rule. The only rule not allowed would be random assignment, for randomness amounts in effect to a nonrule". However, so-called nominal measurement involves arbitrary assignment, and the "permissible transformation" is any number for any other. This is one of the points made in Lord's (1953) satirical paper On the Statistical Treatment of Football Numbers.

Among those who accept the classification scheme, there is also some controversy in behavioural sciences over whether the mean is meaningful for ordinal measurement. In terms of measurement theory, it is not, because the arithmetic operations are not made on numbers that are measurements in units, and so the results of computations do not give numbers in units. However, many behavioural scientists use means for ordinal data anyway. This is often justified on the basis that ordinal scales in behavioural science are really somewhere between true ordinal and interval scales; although the interval difference between two ordinal ranks is not constant, it is often of the same order of magnitude. For example, applications of measurement models in educational contexts often indicate that total scores have a fairly linear relationship with measurements across a range of an assessment. Thus, some argue, that so long as the unknown interval difference between ordinal scale ranks is not too variable, interval scale statistics such as means can meaningfully be used on ordinal scale variables. Statistical analysis software such as PSPP require the user to select the appropriate measurement class for each variable. This ensures that subsequent user errors cannot inadvertently perform meaningless analyses (for example correlation analysis with a variable on a nominal level).

L. L. Thurstone made progress toward developing a justification for obtaining interval-level measurements based on the law of comparative judgment. For a common application of the law, see the Analytic Hierarchy Process. Further progress was made by Georg Rasch (1960), who developed the probabilistic Rasch model that provides a theoretical basis and justification for obtaining interval-level measurements from counts of observations such as total scores on assessments.

Another issue is derived from Nicholas R. Chrisman's article "Rethinking Levels of Measurement for Cartography", in which he introduces an expanded list of levels of measurement to account for various measurements that do not necessarily fit with the traditional notion of levels of measurement. Measurements bound to a range and repeat (like degrees in a circle, time, etc.), graded membership categories, and other types of measurement do not fit to Steven's original work, leading to the introduction of 6 new levels of measurement leading to: (1) Nominal, (2) Graded membership, (3) Ordinal, (4) Interval, (5) Log-Interval, (6) Extensive Ratio, (7) Cyclical Ratio, (8) Derived Ratio, (9) Counts and finally (10) Absolute. The extended levels of measurement are rarely used outside of academic geography.